The way I see it this is time spent between adventures. This assumes that not every day of a character's life is roleplayed but that considerable time passes between each adventure (weeks, months). Some RPGs, as has been mentioned in this thread too, have rules for figuring out what the PCs have done since the last adventure. These could even provide the PC with some benefits if the GM allows it.

The Ultimate Campaign book for Pathfinder has a pretty nicely developed downtime system that I plan to try out in my next campaign. First, it defines rules for gaining and using capital (an abstraction of the goods, influence, labor, and magic generated and consumed by downtime activities) and what the phases are for a downtime day. Then it gives a list of downtime activities and how they work in this system:

Add spells to your spellbook

Construct buildings

Craft magic items

Craft mundane items

Earn capital

Earn XP [used to catch up with other PCs, if you're lagging behind]

Gather information

Heal others

Lead your kingdom [uses the kingdom-building rules, found in another chapter]

Promote a business

Replace your animal companion

Replace your familiar

Recruit for an organization

Research a spell

Research facts and lore

Rest

Retrain

Run a business

Scheme for an upcoming adventure [spend capital and time to gain a bonus on specific future checks]

Train an animal

Many of these are right out of the Core Rulebook. Some activities involve creating and using buildings or organizations, so the next section details how that works (buildings are defined as a set of rooms, with specific game functions, and organizations are similarly built of teams of workers). The final section consists of lists of random events that can make downtime more interesting. The full rules can be found in the PF SRD here.

This system was designed for a medieval/renaissance setting, but could be adapted to modern or future games with some effort. The capital system is abstract enough that different forms of currency wouldn't be an insurmountable obstacle. It also might take some work to adapt the room/team system to later tech levels, but since each unit is defined in terms of skill use and earning capital, the basic functions of many of them won't appreciably change with tech level.